Given below are two statements:
Statement I : Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
Statement II : Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's surface, if h = d.
In the light of above statements, choose the most appropriate answer from the options given below
Statement I : Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
Statement II : Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's surface, if h = d.
In the light of above statements, choose the most appropriate answer from the options given below
- A.Statement I is incorrect but statement II is correct
- B.Both Statement I and Statement II are incorrect
- C.Both Statement I and II are correct
- D.Statement I is correct but statement II is incorrect
Show answer and solution
Correct option: D
Solution
Statement I is correct: above the surface, g decreases as g/( 1 + h/R)², and below the surface g decreases as g(1 - d/R), so in both directions g reduces from its surface value.
Statement II is false: at height h, gh ≈ g(1 - 2h/R) (using binomial approximation), while at depth d, gd = g(1 - d/R). For h = d, gh < gd since the factor of 2 makes the reduction at height greater than at the same depth. The two values are only equal if 2h/R = d/R, i.e., d = 2h, not when h = d.
Statement II is false: at height h, gh ≈ g(1 - 2h/R) (using binomial approximation), while at depth d, gd = g(1 - d/R). For h = d, gh < gd since the factor of 2 makes the reduction at height greater than at the same depth. The two values are only equal if 2h/R = d/R, i.e., d = 2h, not when h = d.
[JEE Main 2023 · 24 Jan · Shift 2]